It becomes a real problem because the carrier name and SCAC in the carrier box is who payment is released to. So it can be a big mess.
When one is the primary lane award from a shipper this doesn't seem to be a problem. But when a shipper does something like a broadcast dispatch to its base to cover a load (usually because primary isn't performing) you end up with multiple players trying to cover the same load. We avoid it whenever we can, needless to say.
Certain shippers are notorious for it.